O. Polit

Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis

The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C 1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and torsional studies. The geometric nonlinearity based on von Karman’s assumptions is incorporated in the formulation while retaining the linear behavior for the material. The finite element employed here is based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam. The transverse shear deformation in the form of trigonometric sine function is introduced in the formulation to define the transverse shear strain. The governing equations of motion for the dynamic analysis are obtained using Lagrange’s equation of motion. The solution for nonlinear equations is sought by using an algorithmdirect iteration technique suitably modified for eigenvalue problems, based on the QR algorithm. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear modulus and thickness of the core of the sandwich beam, aspect ratios, boundary conditions, and lay-up in the case of laminates on the system loss factors. q 1999 Elsevier Science Ltd. All rights reserved.

A C1 finite element including transverse shear and torsion warping for rectangular sandwich beams

A new three-noded C1 beam finite element is derived for the analysis of sandwich beams. The formulation includes transverse shear and warping due to torsion. It also accounts for the interlaminar continuity conditions at the interfaces between the layers, and the boundary conditions at the upper and lower surfaces of the beam. The transverse shear deformation is represented by a cosine function of a higher order. This allows us to avoid using shear correction factors. A warping function obtained from a three-dimensional elasticity solution is used in the present model. Since the field consistency approach is accounted for interpolating the transverse strain and torsional strain, an exact integration scheme is employed in evaluating the strain energy terms. Performance of the element is tested by comparing the present results with exact three-dimensional solu-tions available for laminates under bending, and the elasticity three-dimensional solution deduced from the de Saint-Venant solution including both torsion with warping and bending. In addition, three-dimensional solid finite elements using 27 noded-brick elements have been used to bring out a reference solution not available for sandwich structures having high shear modular ratio between skins and core. A detailed parametric study is carried out to show the effects of various parameters such as length-to-thickness ratio, shear modular ratio, boundary conditions, free (de Saint-Venant) and constrained torsion. Copyright

Two higher order Zig-Zag theories for the accurate analysis of bending, vibration and buckling response of laminated plates by radial basis functions collocation and a unified formulation

In this article, we combine the Carreras Unified Formulation, CUF (Carrera E. Theories and Finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking. Arch. Comput. Methods Eng., 2003; 10: 215–297.) and a radial basis function collocation technique for predicting the static deformations, free vibrations and buckling behavior of thin and thick cross-ply laminated plates. We develop by the CUF two Zig-Zag theories according to Murakamis Zig-Zag function. Both theories account for through-the-thickness deformations, allowing the analysis of thick plates. The accuracy and efficiency of this collocation technique for static, vibration, and buckling problems are demonstrated through numerical examples.

An Efficient Finite Shell Element for the Static Response of Piezoelectric Laminates

This study presents a novel finite element (FE) for shell structures including piezoelectric actuators and sensors. Based on a conventional 8-node shell formulation and the classical displacement-based variational formulation, the present element has an enriched description of the transverse kinematics in order to consistently retain the full three-dimensional (3D) piezoelectric coupling. Furthermore, a layer-wise description of the electric degrees of freedom permits to account for embedded piezoelectric actuators and sensors. The robustness of the FE is enhanced by referring to an established technique that avoids transverse shear locking and membrane locking. Numerical results are given which validate the present implementation and highlight the efficiency and accuracy of the proposed formulation. Additionally, some new reference solutions for the static behavior of piezoelectric shells are provided by means of 3D FE computations with a commercial software.

A Refined Sinus Finite Element Model for the Analysis of Piezoelectric-Laminated Beams

A three-nodded beam finite element is developed for the analysis of composite-laminated beams with distributed piezoelectric sensor/actuator layers. The mechanical part of the proposed element is based on the refined sinus model. This element does not require shear correction factor and ensures continuity conditions for displacements, transverse shear stresses as well as boundary conditions on the upper and lower surfaces of the beam. This conforming finite element is totally free of shear locking, and the number of mechanical unknowns is independent of the number of layers. For each piezoelectric layer, a high-order electrical potential field is considered. The virtual work principle leads to a derivation that could include dynamic analysis. However, in this study, only static problems have been considered. Comparison of numerical results obtained from this formulation with previous works shows that the present finite element is suitable for predicting fully coupled behaviors of both thick and thin smart-laminated beams under mechanical and electrical loadings.

Analysis of sandwich plates by radial basis functions collocation, according to Murakami's Zig-Zag theory

In this article, the static analysis of sandwich plates is performed by radial basis functions collocation, according to the Murakamis Zig-Zag function theory. The Murakamis Zig-Zag function theory accounts for through-the-thickness deformation, by considering a Zig-Zag evolution of the transverse displacement with the thickness coordinate. The equations of motion and the boundary conditions are obtained by the Carreras unified formulation, and further interpolated by collocation with radial basis functions.

Assessment of free-edge singularities in composite laminates using higher-order plate elements

Abstract The capabilities and limitations of refined two-dimensional (2D) composite plate elements are discussed with respect to the stress concentration problem occurring at traction-free edges. Classical displacement-based and advanced partially mixed finite elements are formulated according to Carrera’s Unified Formulation (CUF). Rectangular laminates are analyzed under extension and bending loading, where the attention is focused on the local stress response at the free edges. Present results are compared with reference results available in the literature and a 3D finite element model. A power law representation for a singular stress field is used to fit the obtained stresses in the vicinity of the free edge, and the parameters are used to assess the CUF elements and to compare the free-edge effect occurring in extension and bending.

Sensitivity Analysis of Thickness Assumptions for Piezoelectric Plate Models

This article compares different axiomatic 2D theories for linear homogeneous piezoelectric plates. Simple actuator and sensor configurations are considered of thin and thick piezoelectric ceramics working either in transverse extension (31 mode) or in shear mode (15 mode). By generalizing a previously established unified formulation, a large number of different through-thickness approximations for the in-plane displacement, the transverse displacement and the electrostatic potential are introduced. Additionally, either full 3D constitutive law or reduced constitutive equations accounting for a vanishing transverse normal stress are employed in these plate theories. By referring to an analytical Naviertype closed-form solution, a systematic assessment of various 2D models is performed. The proposed sensitivity analysis of plate theories with respect to their electromechanical response can serve as a useful guide for choosing appropriate models depending on the piezoelectric polarization scheme, the use as sensor or actuator, and the plate thickness.

A new laminated triangular finite element assuring interface continuity for displacements and stresses

The objective of this paper is to present a new 81-degrees-of-freedom finite element for geometrically and materially linear elastic multilayered composite, moderately thick plates. The element is a six nodes C1 triangular element based on a new kind of kinematics and built from Argyris interpolation for bending, and Ganev interpolation for membrane displacements and transverse shear rotations. The kinematics allow both, the continuity conditions for displacements and transverse shear stresses at the interfaces between layers of a laminated structure, and the boundary conditions at the upper and lower surfaces of the plates, to be exactly ensured. The representation of the transverse shear strains by cosine functions allows one to avoid shear correction factors. The element performances are evaluated on some standard plate tests and also in comparison with an exact three-dimensional solution for multilayered plates both for statics and dynamics.

Bending and vibration of laminated plates by a layerwise formulation and collocation with radial basis functions

This article addresses the static deformations and free vibration analysis of laminated composite and sandwich plates by collocation with radial basis functions, according to a layerwise formulation. The present layerwise approach accounts for through-the-thickness deformations. The equations of motion and the boundary conditions are obtained by the Carrera’s Unified Formulation, and further interpolated by collocation with radial basis functions.